Quantum interference effect (QIE) is the key to the quantum nature of a system. In an atom-field interacting quantum system, QIE enables rich interesting physics and applicable phenomena, such as electromagnetically induced transparency (EIT) [1]}, [2]} and Autler-Townes splitting (ATS) [3]}. Both of them are observed with a transparency window induced by the un-modulated coherent drive fields, though they originate from controversial mechanisms that have been studied over decades in various systems and scenarios  [4]}, [5]}, [6]}. In the above un-modulated systems, the properties of QIE can be adjusted by manipulating the properties of the system, which is relatively difficult. Few studies have been done to alter the properties of QIE by using tunable auxiliary energy levels or phase-modulated fields [7]}, [8]}, [9]}. Recently, with the rising interest in Floquet systems, rich novel physics are discovered, where the Floquet parameters (such as modulation period, modulation scheme, etc.) may be useful tools for tuning the properties of QIEs. However, to our knowledge, the QIEs in the Floquet controlled systems have not been adequately studied [10]}, especially the effect of the modulation period on the properties of QIEs.
